Pre-Publicación 2026-30
Rodrigo Carrasco Jofré, Mauricio Sepúlveda, Jaime Muñoz-Rivera:
Analytic and Gevrey regularity for a hybrid thermoelastic Euler–Bernoulli beam with singular interactions
Abstract:
We investigate the regularity and stability properties of a hybrid Euler–Bernoulli beam consisting of elastic and thermoelastic components, with type III thermoelasticity, discontinuous material coefficients, and singular pointwise interactions modeled by Dirac distributions and their derivatives. The beam is dynamically coupled at one endpoint to a rigid tip body with mass, rotational inertia, and an offset center of mass, giving rise to a PDE–ODE system with dynamic boundary conditions. Using frequency-domain methods and high-frequency resolvent estimates, we show that when the thermoelastic mechanism acts throughout the beam, the associated C0-semigroup is analytic, despite the presence of singular interactions and the dynamic coupling with the tip body. In contrast, when the thermoelastic effects are confined to a proper subinterval, analyticity is lost and the semigroup is of Gevrey class 2. In both configurations, the system is exponentially stable. These results show that the transition from analyticity to Gevrey regularity induced by the localization of the thermoelastic mechanism persists in the presence of both singular interactions and dynamic tip-body coupling.
